Is a Phychic Dragonborn a viable build?

...What? No melee, archery or magic in combat, just telekinesis? Seriously?

you might run out of stuff to throw

Carry around that one bear trap for the whole game...

Not even on the easiest setting, no.

Why wouldn't it be?

What is the damage like?

i don't even have telekinesis but i can't imagine the damage is great. but maybe in the next elderscrolls there can be a "psychic" school of magic, i mean we already have unrelenting force, work around that bethesda haha

I have not used it that much, but I hear there are certain trap items like open bear traps that do decent damage. However if you pick up a tankard and throw it at someone it will not do much. Also it is hard to grind alteration by itself until you actual get telekinesis (then it is easy). You can do it by e.g. repeatedly casting mage armor while pacifying and annoying some animal, but it would be quite a feat to do the whole game using only telekinesis.

It'd be ridiculously annoying to fight that way. There is an Improved Telekinesis mod on the Nexus though that causes thrown items to move faster and do more damage, that might make it bearable.

For a psionic playthrough though, I'd use both Illusion and Alteration to simulate mind affecting powers and kinetic barriers, paralyzing mindblasts, and straight up telekinesis.

My psionic assassin also uses Bound Swords as Mindblades.

Unless your playing as Jean Grey, no.